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					  Hydraulic System
Modeling and Analysis


      Guangbin Sun

       5/13/2011
   1. Modeling Stick-Slip Friction
              in valve
• Phenomenon: at low freq., pressure
  jump occurs when flow changes
  signs; at some freq., oscillation
  occurs.
1. Modeling Stick-Slip Friction
           in valve
                      42       F=0.2225hz Mag=100             Torque          40




                      41


                                                                              39


                      40




                      39                                                      38




                      38
         L_HFE_rtrq




                                                                              37


                      37




                      36                                                      36




                      35


                                                                              35


                      34




                      33                                                      34

                      40
                           0
                               F=0.4952hz Mag=300
                                  5        10       15        20       25
                                                                             39
                                                                                   -1      -0.5   0   0.5         1




                      39                                                    38.5




                      38                                                     38
 L_HFE_rtrq




                      37                                                    37.5




                      36                                                     37




                      35                                                    36.5




                      34                                                     36
                           0           5                 10            15           -0.5          0         0.5
1. Modeling Stick-Slip Friction
           in valve
Why friction of valve?

Because this phenomena occurs only at low frequency, it should be the
effects of valve friction(especially static friction).
1. Modeling Stick-Slip Friction
           in valve
1. Modeling Stick-Slip Friction
           in valve
                          1. Modeling Stick-Slip Friction
                                     in valve
                                            data                                                                                    data

           40                                                                                      40
torq(NM)




                                                                                        torq(NM)
           35                                                                                      35



           30                                                                                      30
                0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
                                         time(0.001s)                           4                                                time(0.001s)                           4
                                                                             x 10                                                                                    x 10
                                           model                                                                                   model

           40                                                                                      40
torq(NM)




                                                                                        torq(NM)
           35                                                                                      35



           30                                                                                      30
                0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
                                         time(0.001s)                           4                                                time(0.001s)                           4
                                                                             x 10                                                                                    x 10




                           f=0.1hz; mag=100                                                                       f=0.1492hz; mag=100
                          1. Modeling Stick-Slip Friction
                                     in valve
                                            data                                                                                     data
           45                                                                                      45


           40                                                                                      40
torq(NM)




                                                                                        torq(NM)
           35                                                                                      35


           30                                                                                      30
                0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2    0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
                                         time(0.001s)                           4                                                 time(0.001s)                           4
                                                                             x 10                                                                                     x 10
                                           model                                                                                    model
           45                                                                                      45


           40
torq(NM)




                                                                                                   40




                                                                                        torq(NM)
           35                                                                                      35


           30                                                                                      30
                0   0.2   0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2                   0   0.2    0.4   0.6   0.8      1     1.2   1.4   1.6   1.8          2
                                         time(0.001s)                           4
                                                                                                                                  time(0.001s)                           4
                                                                             x 10                                                                                     x 10



                          f=0.2225hz; mag=200                                                                     f=0.3319hz; mag=300
                    1. Modeling Stick-Slip Friction
                               in valve
                                 data                                                           data
           40                                                           42

                                                                        40
           38
torq(NM)




                                                             torq(NM)
                                                                        38
           36
                                                                        36

           34                                                           34
                0      5000                  10000   15000                   0        5000                  10000   15000
                              time(0.001s)                                                   time(0.001s)
                                 model                                                          model
           40                                                           42

                                                                        40
           38
torq(NM)




                                                             torq(NM)
                                                                        38
           36
                                                                        36

           34                                                           34
                0      5000                  10000   15000                   0        5000                  10000   15000
                              time(0.001s)                                                   time(0.001s)



                    f=0.4592hz; mag=300                                          f=0.7386hz; mag=400
                    1. Modeling Stick-Slip Friction
                               in valve
                                data                                                          data
           40                                                          50


                                                                       40
torq(NM)




                                                            torq(NM)
           35
                                                                       30


           30                                                          20
                0     5000                  10000   15000                   0       5000                  10000   15000
                             time(0.001s)                                                  time(0.001s)
                                model                                                         model
                                                                       50
           45
torq(NM)




                                                            torq(NM)
                                                                       40

           40
                                                                       30


           35                                                          20
                0     5000                  10000   15000                   0       5000                  10000   15000
                             time(0.001s)                                                  time(0.001s)



                    f=0.7386hz; mag=800                                         f=1.1018hz; mag=800
                    1. Modeling Stick-Slip Friction
                               in valve
                                data                                                           data
           60                                                          60
torq(NM)




                                                            torq(NM)
           40                                                          40


           20                                                          20

                0     5000                  10000   15000                   0        5000                  10000   15000
                             time(0.001s)                                                   time(0.001s)
                                model                                                          model

           60                                                          60




                                                            torq(NM)
torq(NM)




           40                                                          40


           20                                                          20

                0     5000                  10000   15000                   0        5000                  10000   15000
                             time(0.001s)                                                   time(0.001s)


                    f=1.6436hz; mag=800                                         f=2.4517hz; mag=400
2. Modeling Piston Friction
                 2. Modeling Piston Friction
                            data                                                      data

           40                                                      40
torq(NM)




                                                        torq(NM)
           35                                                      35


           30                                                      30

            0     5000                  10000   15000               0       5000                  10000   15000
                         time(0.001s)                                              time(0.001s)
                            model                                                     model

           40                                                      40
torq(NM)




                                                        torq(NM)
           35                                                      35


           30                                                      30

            0     5000                  10000   15000               0       5000                  10000   15000
                         time(0.001s)                                              time(0.001s)




                f=0.1hz; mag=100                                        f=0.1492hz; mag=100
                     2. Modeling Piston Friction
                                 data                                                          data
           45                                                           45


           40                                                           40
torq(NM)




                                                             torq(NM)
           35                                                           35


           30                                                           30
                0      5000                  10000   15000                   0       5000                  10000   15000
                              time(0.001s)                                                  time(0.001s)
                                 model                                                         model
           45                                                           45


           40                                                           40
torq(NM)




                                                             torq(NM)
           35                                                           35


           30                                                           30
                0      5000                  10000   15000                   0       5000                  10000   15000
                              time(0.001s)                                                  time(0.001s)



                    f=0.2225hz; mag=200                                          f=0.3319hz; mag=300
                     2. Modeling Piston Friction
                                 data                                                         data
           40                                                           42

                                                                        40
           38
torq(NM)




                                                             torq(NM)
                                                                        38
           36
                                                                        36

           34                                                           34
                0      5000                  10000   15000                   0      5000                  10000   15000
                              time(0.001s)                                                 time(0.001s)
                                 model                                                        model
           40                                                           42

                                                                        40
           38
torq(NM)




                                                             torq(NM)
                                                                        38
           36
                                                                        36

           34                                                           34
                0      5000                  10000   15000                   0      5000                  10000   15000
                              time(0.001s)                                                 time(0.001s)



                    f=0.4952hz; mag=300                                          f=0.7386hz; mag=400
                     2. Modeling Piston Friction
                                data                                                          data
                                                                       50
           45
torq(NM)




                                                            torq(NM)
                                                                       40
           40


           35                                                          30

                0     5000                  10000   15000                   0       5000                  10000   15000
                             time(0.001s)                                                  time(0.001s)
                                model                                                         model
                                                                       50
           45
torq(NM)




                                                            torq(NM)
                                                                       40
           40


           35                                                          30

                0     5000                  10000   15000                   0       5000                  10000   15000
                             time(0.001s)                                                  time(0.001s)




                    f=0.7386hz; mag=800                                         f=1.1018hz; mag=800
                     2. Modeling Piston Friction
                                data                                                          data
           60                                                          60
torq(NM)




                                                            torq(NM)
           40                                                          40


           20                                                          20

                0     5000                  10000   15000                   0       5000                  10000   15000
                             time(0.001s)                                                  time(0.001s)
                                model                                                         model
           60                                                          60
torq(NM)




                                                            torq(NM)
           40                                                          40


           20                                                          20

                0     5000                  10000   15000                   0       5000                  10000   15000
                             time(0.001s)                                                  time(0.001s)




                    f=1.6436hz; mag=800                                         f=2.4517hz; mag=400
                3. Valve & Piston Friction together
                                data                                                       data

           40                                                          40
torq(NM)




                                                            torq(NM)
           35                                                          35


           30                                                          30

            0         5000                  10000   15000               0        5000                  10000   15000
                             time(0.001s)                                               time(0.001s)
                                model                                                      model

           40                                                          40
torq(NM)




                                                            torq(NM)
           35                                                          35


           30                                                          30

            0         5000                  10000   15000               0        5000                  10000   15000
                             time(0.001s)                                               time(0.001s)




                   f=0.1hz; mag=100                                         f=0.1492hz; mag=100
                    3. Valve & Piston Friction together
                                   data                                                          data
           45                                                             45


           40
torq(NM)




                                                                          40




                                                               torq(NM)
           35                                                             35


           30                                                             30
                0        5000                  10000   15000                   0       5000                  10000   15000
                                time(0.001s)                                                  time(0.001s)
                                   model                                                         model
           45                                                             45


           40                                                             40
torq(NM)




                                                               torq(NM)
           35                                                             35


           30                                                             30
                0        5000                  10000   15000                   0       5000                  10000   15000
                                time(0.001s)                                                  time(0.001s)



                      f=0.2225hz; mag=200                                          f=0.3319hz; mag=300
                    3. Valve & Piston Friction together
                                   data                                                           data
           40                                                             42

                                                                          40
           38




                                                               torq(NM)
torq(NM)




                                                                          38
           36
                                                                          36

           34                                                             34
                0        5000                  10000   15000                   0        5000                  10000   15000
                                time(0.001s)                                                   time(0.001s)
                                   model                                                          model
           40                                                             42

                                                                          40
           38




                                                               torq(NM)
torq(NM)




                                                                          38
           36
                                                                          36

           34                                                             34
                0        5000                  10000   15000                   0        5000                  10000   15000
                                time(0.001s)                                                   time(0.001s)


                      f=0.4952hz; mag=300                                          f=0.7386hz; mag=400
                    3. Valve & Piston Friction together
                                  data                                                          data
                                                                         50
           45




                                                              torq(NM)
torq(NM)




                                                                         40
           40


           35                                                            30

                0       5000                  10000   15000                   0       5000                  10000   15000
                               time(0.001s)                                                  time(0.001s)
                                  model                                                         model
                                                                         50
           45
torq(NM)




                                                              torq(NM)
                                                                         40
           40


           35                                                            30

                0       5000                  10000   15000                   0       5000                  10000   15000
                               time(0.001s)                                                  time(0.001s)


                      f=0.7386hz; mag=800                                         f=1.1018hz; mag=800
                    3. Valve & Piston Friction together
                                 data                                                        data

           60                                                           60




                                                             torq(NM)
torq(NM)




           40                                                           40


           20                                                           20

                0      5000                  10000   15000                   0     5000                  10000   15000
                              time(0.001s)                                                time(0.001s)
                                 model                                                       model

           60                                                           60




                                                             torq(NM)
torq(NM)




           40                                                           40


           20                                                           20

                0      5000                  10000   15000                   0     5000                  10000   15000
                              time(0.001s)                                                time(0.001s)




                      f=1.6436hz; mag=800                                        f=2.4517hz; mag=400
                        4. Moment Arm
                                     Moment Arm
                0.044
                                                              Mine
                                                              Previous
                0.042



                 0.04
X dot/ th dot




                0.038



                0.036



                0.034



                0.032
                     -1   -0.5   0       0.5        1   1.5              2
                                     Angle [rad.]



                There’re 2 parameters in previous version
                (hfe.m) which I think are wrong.
                L5=0.27(should be 0.2748); th5=th4-
                80*pi/180(should be 75.5);
4. Moment Arm
                5. Simulate Complex Model
•Complex Model--Physics-based Model


                                                                                  
                Assume x1   ; x 2   ; x 3  p1 ; x 4  p2 ; x 5  xv ; x 6  xv ;
                 
                x1  x2
                      L                             mgl sin( x1 )
                x2       [( x3   x4 ) Ap  F f ] 
                       Ja                                 Ja
                    E1' ( x3 )
                x3             [Q1 ( x3 , x5 )  Ap c1 x2  K Li ( x4  x3 )]
                     V1 ( x1 )
                     '
                     E2 ( x4 )
                x4            [Q2 ( x4 , x5 )   Ap c1 x2  K Li ( x4  x3 )]
                     V2 ( x1 )
                 
                x5  x6
                 
                x6  2n x6  n x5  Ku (approximated )
                                 2


                                                                           x2
                where, Ff   x2  sign( x2 )[ Fc 0  Fs 0 exp(              )]
                                                                           cs
5. Simulate Complex Model
        5. Simulate Complex Model
           Values of Coefficients
names    description         values        units
Ps       Supply pressure     20684271.87   Pa
PT       Return pressure     Ps/20         Pa
zeta     Damping             0.5           ___
         coefficient of
         valve
wn       Natural frequency   200*2*pi      rad/s
         of valve
Vpl      Oil volume in      1.7093e-005    m^3
         pipelines between
         valve and cylinder
K        Valve gain          0.0381        ___
m        Mass of load        12.7002       kg
l        Length of CoM       0.5181        m
         from pivot
Ap       Piston area         1.9793e-004   m^2
alpha    Piston area ratio   0.635         ___
              5. Simulate Complex Model
                 Values of Coefficients
names          description         values        units
               Param for viscous 3200
               friction
               Param for           unused
               coulomb friction
               Param for static    unused
               friction
               Param for static    unused
               friction(Stribeck
               velocity)
               Flow coefficient of 1.4982e-6
               valve
        KLi    Internal leakage    1.0390e-013
               coefficient
               Moment Arm          changing      m
        L      Actuator length     changing      m
    Emax       Maximum bulk        1.3410e+009   Pa
                                5. Simulate Complex Model
                                                       (Last Work) Around
                                                       different angles
                  4
                         Commanded valve -> Torq                                                      Commanded valve -> Torq
                10                                                                          100
                                                           x1=-0.5                                                                  x1=-0.5
                                                           x1=0                                                                     x1=0
                                                           x1=0.5                                                                   x1=0.5
                                                           x1=1                              50
                                                                                                                                    x1=1
                                                           x1=1.5                                                                   x1=1.5
                  3
                10




                                                                          Phase (degrees)
Log Magnitude




                                                                                               0




                                                                                             -50
                  2
                10


                                                                                            -100



                  1
                10                                                                          -150
                    -1    0                        1                  2                          -1    0                        1              2
                  10     10                   10                     10                        10     10                   10                 10
                              Log Frequency                                                                Log Frequency
                                 5. Simulate Complex Model— no gravity (V
                                            changing with angles)
                                    Commanded valve -> Torq
                    3                                                                                              Commanded valve -> Torq
                  10
                                                                                                         100
                                                                    x1=-0.5                                                                      x1=-0.5
                                                                    x1=0                                                                         x1=0
                                                                    x1=0.5                                                                       x1=0.5
                                                                    x1=1                                  50
                                                                                                                                                 x1=1
                                                                    x1=1.5                                                                       x1=1.5
                    2
                  10




                                                                                       Phase (degrees)
Log Magnitude




                                                                                                            0




                                                                                                          -50
                    1
                  10


                                                                                                         -100




                    0                                                                                    -150
                  10                                                                                          -1     0                       1              2
                       -1             0                       1                2                            10     10                   10
                                                                                                                    Commanded valve -> Vel                 10
                    10
                     1
                                                           10
                                    10 Commanded valve -> vel                 10
                  10                                                                                      50           Log Frequency
                                          Log Frequency
                                                                    x1=-0.5                                                                      x1=-0.5
                                                                    x1=0                                                                         x1=0
                                                                    x1=0.5                                  0                                    x1=0.5
                       0                                            x1=1                                                                         x1=1
                  10                                                                                                                             x1=1.5
                                                                    x1=1.5
                                                                                                          -50
                                                                                       Phase (degrees)
  Log Magnitude




                       -1                                                                                -100
                  10


                                                                                                         -150

                       -2
                  10
                                                                                                         -200



                       -3                                                                                -250
                                                                                                              -1     0                       1              2
                  10                                                                                        10     10                    10                10
                            -1        0                         1                  2
                       10           10                     10                 10                                         Log Frequency
                          5. Simulate Complex Model-- no gravity (V
                                    changing with angles)
                                Commanded valve -> pos
                 0                                                                                   Commanded valve -> pos
                10
                                                                                           -50
                                                         x1=-0.5
                                                                                                                                  x1=-0.5
                                                         x1=0
                                                                                                                                  x1=0
                                                         x1=0.5                           -100                                    x1=0.5
                                                         x1=1                                                                     x1=1
                                                         x1=1.5                                                                   x1=1.5
                                                                                          -150




                                                                        Phase (degrees)
Log Magnitude




                 -1
                10                                                                        -200



                                                                                          -250



                                                                                          -300


                 -2
                10                                                                        -350
                      -1                    0                       1                          -1    0                        1              2
                     10                   10                       10                        10     10                   10                 10
                                    Log Frequency                                                        Log Frequency
                         5. Simulate Complex Model—with
                                gravity(V=constant)
                  3
                         Commanded valve -> Torq                                                  Commanded valve -> Torq
                10                                                                      100
                                                       x1=-0.5                                                                  x1=-0.5
                                                       x1=0                                                                     x1=0
                                                       x1=0.5                                                                   x1=0.5
                                                                                         50
                                                       x1=1                                                                     x1=1
                                                       x1=1.5                                                                   x1=1.5
                  2
                10




                                                                      Phase (degrees)
Log Magnitude




                                                                                           0




                                                                                         -50
                  1
                10


                                                                                        -100



                  0
                10                                                                      -150
                    -1    0                        1              2                          -1    0                        1              2
                  10     10                   10                 10                        10     10                   10                 10
                              Log Frequency                                                            Log Frequency
                                 5. Simulate Complex Model—moment arm
                   10
                        3                   changing with angles
                                     Commanded valve -> Torq
                                                                                                    150
                                                                                                              Commanded valve -> Torq

                                                                                                                                                x1=-0.5
                                                                   x1=-0.5
                                                                   x1=0                                                                         x1=0
                                                                   x1=0.5                           100                                         x1=0.5
                                                                   x1=1                                                                         x1=1
                                                                   x1=1.5                                                                       x1=1.5
                        2
                   10                                                                                50




                                                                                  Phase (degrees)
   Log Magnitude




                                                                                                       0


                        1
                   10                                                                                -50



                                                                                                    -100


                        0
                   10                                                                               -150
                       -1             0                        1              2                          -1    0                        1                  2
                     10              10                    10                10                        10     10                      10                  10
                                          Log Frequency                                                               Log Frequency
                                      Commanded valve -> vel                                                       Commanded valve -> Vel
                    2                                                                               150
                   10
                                                                   x1=-0.5                                                                       x1=-0.5
                                                                   x1=0                             100                                          x1=0
                    1
                   10                                              x1=0.5                                                                        x1=0.5
                                                                   x1=1                                                                          x1=1
                                                                                                      50
                                                                   x1=1.5                                                                        x1=1.5
                    0
                   10
                                                                                                       0
                                                                                  Phase (degrees)
Log Magnitude




                    -1
                   10                                                                                -50


                    -2                                                                              -100
                   10

                                                                                                    -150
                    -3
                   10
                                                                                                    -200

                    -4
                   10                                                                               -250
                            -1        0                        1              2
                        10           10                    10                10                          -1        0                        1                  2
                                                                                                       10     10                       10                  10
                                          Log Frequency
                         5. Simulate Complex Model—Different bulk
                                     modulus(last work)


                  4
                           Commanded valve -> Torq                                                       Commanded valve -> Torq
                10                                                                             100
                                                         Emax=1.341e9                                                                  Emax=1.341e9
                                                         0.5Emax                                                                       0.5Emax
                                                         2Emax                                                                         2Emax
                                                                                                50

                  3
                10




                                                                             Phase (degrees)
Log Magnitude




                                                                                                  0




                                                                                                -50
                  2
                10


                                                                                               -100



                  1
                10                                                                             -150
                    -1      0                        1                   2                          -1    0                        1                   2
                  10       10                   10                      10                        10     10                   10                      10
                                Log Frequency                                                                 Log Frequency
                           5. Simulate Complex Model—Different bulk
                                       modulus(last work)

                 2
                            Commanded valve -> Angle position                                                   Commanded valve -> Angle position
                10                                                                                     -50
                                                                Emax=1.341e9                                                                        Emax=1.341e9
                                                                0.5Emax                                                                             0.5Emax
                 1                                                                                    -100
                10                                              2Emax                                                                               2Emax


                                                                                                      -150
                 0
                10




                                                                                    Phase (degrees)
Log Magnitude




                                                                                                      -200
                 -1
                10
                                                                                                      -250
                 -2
                10
                                                                                                      -300

                 -3
                10                                                                                    -350


                 -4
                10                                                                                    -400
                      -1         0                      1                       2                          -1        0                      1                       2
                     10        10                     10                       10                        10        10                     10                       10
                                     Log Frequency                                                                       Log Frequency
                5. Simulate Complex Model—Different length between
                             CoG and hip pivot(last work)



                  4
                         Commanded valve -> Torq                                                           Commanded valve -> Torq
                10                                                                               100
                                                       CoG2Pivot=0.5181                                                                  CoG2Pivot=0.5181
                                                       0.5CoG2Pivot                                                                      0.5CoG2Pivot
                                                       2CoG2Pivot                                                                        2CoG2Pivot
                                                                                                  50

                  3
                10




                                                                               Phase (degrees)
Log Magnitude




                                                                                                    0




                                                                                                  -50
                  2
                10


                                                                                                 -100



                  1
                10                                                                               -150
                    -1    0                        1                       2                          -1    0                        1                       2
                  10     10                   10                          10                        10     10                   10                          10
                              Log Frequency                                                                     Log Frequency
                5. Simulate Complex Model—Different length between
                             CoG and hip pivot(last work)

                 2
                           Commanded valve -> Angle position                                                   Commanded valve -> Angle position
                10                                                                                      0
                                                           CoG2Pivot=0.5181                                                                    CoG2Pivot=0.5181
                                                           0.5CoG2Pivot                               -50                                      0.5CoG2Pivot
                 1
                10                                         2CoG2Pivot                                                                          2CoG2Pivot

                                                                                                     -100
                 0
                10
                                                                                                     -150




                                                                                   Phase (degrees)
Log Magnitude




                 -1
                10                                                                                   -200


                 -2
                                                                                                     -250
                10

                                                                                                     -300
                 -3
                10
                                                                                                     -350

                 -4
                10                                                                                   -400
                      -1        0                      1                       2                          -1        0                      1                       2
                     10       10                     10                       10                        10        10                     10                       10
                                    Log Frequency                                                                       Log Frequency
                        conclusion
• About friction:
• Valve and piston frictions together are responsible for the load
  oscillation or jump behavior at low frequency.
• Moment Arm:
• Within the range of 0 to 1 radian, moment arm approximates
  0.0375m with good accuracy.
• System Features of Frequency Response:
• 1. Moment arm and gravity effects are most important,
• 2. Piston and ring volume have less effects for our case,
• 3. Bulk modulus has great effects (conclusion of last work),
• 4. Mass distribution affects dynamics intensively (conclusion of last
  work).
• 5. The dynamics of the system is position-dependent and varies
  obviously when angle limit is approached.
             What next?
• Simulate in
  Matlab/simMechanics,simHydraulics
• The Final Model?
• Turn to control?
Thank you

				
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posted:4/4/2013
language:English
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